All small business jets back to the Citation II in my experience put a small positive pressure at some point prior to take-off, so it's related to pressure bumps, not structure. The B727 had the outflow valves in the shaft and it was explained to me, on rotate the valves could be opened by airflow if the differential were not there causing bumps in the cabin.
OTOH, cabin pressure was a requirement for flight in the C-5 for structural reasons. Unpressurized flight required a Lockheed/USAF waiver.